As shown in Figure,. And object O is at the position (-10,2) with respect to the origin P. The concave mirror `M_(1)` has radius of curvature 30cm. A plane mirror `M_(2)` is kept at a distance of 40cm in front of the concave mirror. Considering first refletion on the concave mirror `M_(1)` and second on the plane mirror `M_(2)`. Find the coordinates of the second image w.r.t. the origin P.

Answer

`(-46,-70)`

Explanation

For `m_(1),u=-10cm, f=-15cm, h=2cm. `
Using mirror formula, `(1)/(v)+(1)/(u)=(1)/(f)`
`rArr (1)/(v)+(1)/(-10)=(1)/(-15)`
`rArr(1)/(v)=(1)/(10)-(1)/(15)=(3-2)/(30)`
`rArrv=30cm`
and `(h_(2))/(h_(1))=(v)/(u)rArr h_(2)=6cm`
The image formed by the plane mirror is `70cm` below the principal axis and `70+6-30=46cm` to the left of the mirror. Therefore, oordinate of `I_(2)` w.r.t. P are `(46,-70)`.